Fibonacci Heaps

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Fibonacci Heaps

Fibonacci heap history. Fredman and Tarjan (1986)I Ingenious data structure and analysis.I Original motivation: O(m + nlogn) shortest path algorithm.

F also led to faster algorithms for MST, weighted bipartite matchingI Still ahead of its time.

Fibonacci heap intuition.I Similar to binomial heaps, but less structured.I Decrease-key and union run in O(1) time.I ”Lazy” unions.

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Fibonacci Heaps: Structure

Fibonacci heap.Set of min-heap ordered trees.

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Fibonacci Heaps: Implementation

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Fibonacci Heaps: Potential Function

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Fibonacci Heaps - Basic Idea

Theorem 1

Max rank of a node in a Fibonacci-tree is O(logφ n), where φ = 1+√

52 .

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Fibonacci Heaps: Insert

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Fibonacci Heaps: Insert

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Fibonacci Heaps: Insert

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Binomial Heap: Union

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Fibonacci Heaps: Union

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Fibonacci Heaps: Delete Min

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Fibonacci Heaps: Delete Min Analysis

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Fibonacci Heaps: Delete Min Analysis

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Fibonacci Heaps: Decrease Key

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Fibonacci Heaps: Decrease Key

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Fibonacci Heaps: Decrease Key

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Fibonacci Heaps: Decrease Key

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Fibonacci Heaps: Decrease Key

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Fibonacci Heaps: Decrease Key

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Fibonacci Heaps: Decrease Key

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Fibonacci Heaps: Decrease Key

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Fibonacci Heaps: Decrease Key Analysis

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Fibonacci Heaps: Delete

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